A Geometric Approach to Modeling and Analysis of Mixed-Dimensional and Multi-Continuum Materials

Explore a geometric approach to modeling and analyzing mixed-dimensional and multi-continuum materials in this SIAM Geosciences webinar. Delve into the deep connections between spatial differential operators like gradient, curl, and divergence, and discover how unifying disparate fields in pure and applied mathematics leads to profound new insights. Learn about the "Finite Element Exterior Calculus" work and its impact on unifying finite element literature. Examine how combining elements from differential geometry and functional analysis reveals shared fundamental structures in complex porous media models, including fractured porous media, multi-continuum models, and low-dimensional inclusions. Gain an accessible introduction to these concepts and understand how various models can be viewed as essentially the same equation on an abstract level.

A Geometric Approach to Modeling and Analysis of Mixed-Dimensional and Multi-Continuum Materials